The Collaborative International Dictionary of English v.0.48:
Approving \Ap*prov"ing\, a. Expressing approbation; commending; as, an approving smile. -- Ap*prov"ing*ly, adv. [1913 Webster]WordNet (r) 3.0 (2006):
approvingly adv 1: in an approving manner; "she nodded approvingly" [ant: disapprovingly]